City, the club the 24-year-old supported as a boy, will play in the Europa League next season after winning the Carling Cup last time around.
However, their relegation prompted Gardner to opt instead for Barclays Premier League football at the Stadium of Light when he signed a three-year deal for an undisclosed fee yesterday.
The newcomer has already set his sights on getting a taste of Europe in a red and white shirt after witnessing manager Steve Bruce's recruitment drive to date, with free signings Keiren Westwood and Sebastian Larsson due to join himself, strikers Connor Wickham and Ji Dong-won, and midfielder Ahmed Elmohamady on Wearside today.
Gardner told SAC TV: "It means that the club wants to go places.
"Obviously, we want to finish as high up the table as we can - we want to be in Europe next year and it's a great task to go and chase.
"It's a good goal for us and we can go and do it, and I am sure we will."
Gardner, who scored 10 times for the Blues last season, revealed it did not take Bruce long to persuade him where his future lay after he headed for the north-east on Wednesday.
He said: "Speaking to him, he said, 'Craig, once you get here, you will love it'. I have been here 24 hours and I am so impressed with the place, the training ground, the staff.
"It's just an absolutely brilliant place to be, and hopefully we will settle down really quickly and I will start hitting the back of the net."
Gardner's arrival was announced just hours after South Korea international Ji completed his own move to Sunderland from Chunnam Dragons.
The 20-year-old is already looking forward to going head-to-head with compatriots Park Ji-sung and Lee Chung-yong when the Black Cats come up against Manchester United and Bolton respectively, although he will be doing them no favours.
He said: "I am so glad to be able to meet other Korean players on such a big stage, but there is no such excuse for the opponent. I will do my best to defeat them.
"I am so satisfied to be able to come to a good club, a nice club in the world's number one league.
"I am happy because I have a chance to challenge the biggest players, and that gives me motivation."
Bruce has made something of a reputation for himself by signing players from all corners of the world and Central and South America in particular.
Recent acquisitions Paulo da Silva, Cristian Riveros and Marcos Angeleri have struggled to make an impact on Wearside, and both the manager and his latest signing know it will take him time to adapt to a different lifestyle and a different type of football.
Ji said: "It will not be easy. I am enjoying the life and studying English. I hope I could be a member of this team within six months."